Relationships between a categorical and a continuous variable

Describing the relationship between categorical and continuous variables is perhaps the most familiar of the three broad categories.

When I was in the fifth grade, my class had to participate in an area-wide science fair. We were to devise our own experiment, perform it, and then present it. For some reason, in my experiment I chose to water some lentil sprouts with tap water and some with alcohol to see if they grew differently.

When I measured the heights and compared the measurements of the teetotaller lentils versus the drunken lentils, I was pointing out a relationship between a categorical variable (alcohol/no-alcohol) and a continuous variable (heights of the seedlings).

Note

Note that I wasn't trying to make a broader statement about how alcohol affects plant growth. In the grade-school experiment, I was just summarizing the differences in the heights of those plants—the ones that were in the experiment. In order to make statements...